Erik Kusch, PhD Student
Department of Biology
Section for Ecoinformatics & Biodiversity
Center for Biodiversity Dynamics in a Changing World (BIOCHANGE)
Aarhus University
18/12/2020
[Study Group] Bayesian Statistics with the Rethinking Material 1
18/12/2020
[Study Group] Bayesian Statistics with the Rethinking Material 2
3b, 1w:
9 ways
Bag with 4 marbles of two colours.
Draw with replacement.
Obtain sequence b-w-b.
What’s in the bag?
1b, 3w:
3 ways
Comparing all possibilities enables a selection of the most plausible.
2b, 2w:
8 ways
18/12/2020
[Study Group] Bayesian Statistics with the Rethinking Material 3
Adding prior information to our data can greatly
improve our understanding of the world.
What do we do when we don’t have prior information?
18/12/2020
[Study Group] Bayesian Statistics with the Rethinking Material 4
Proportion of blue marbles
Comparing absolute numbers is difficult and potentially uninformative.
Instead, we compare probabilities/plausabilities.
18/12/2020
[Study Group] Bayesian Statistics with the Rethinking Material 5
Grid approximation
Quadratic approximation
Markov Chain Monte Carlo
(MCMC)
18/12/2020
[Study Group] Bayesian Statistics with the Rethinking Material 6
Variables
Causal
Relationships
between
variables
Joint Prior
MODEL
18/12/2020
[Study Group] Bayesian Statistics with the Rethinking Material 7
18/12/2020
[Study Group] Bayesian Statistics with the Rethinking Material 8
Method
Grid Approximation
Quadratic Approximation
Markov Chain Monte Carlo
Applicability
Few parameters
Models with unified posterior
distributions
All Models
Rationale
“Calculate posterior
distribution(s) at regular
intervals”
“Find the peak of the
posterior distribution and,
assuming it to be Gaussian,
calculate the slope /
standard deviation around it”
“Calculate random samples of the
posterior distribution and build
consensus on the distribution from
this”
18/12/2020
[Study Group] Bayesian Statistics with the Rethinking Material 9
Variables
Causal
Relationships
between
variables
Joint Prior
MODEL
Joint Posterior
18/12/2020
[Study Group] Bayesian Statistics with the Rethinking Material 10
Distributions contain more information than point estimates.
Intervals can only
be trusted when the
model can be
trusted.
18/12/2020
[Study Group] Bayesian Statistics with the Rethinking Material 11
Variables
Causal
Relationships
between
variables
Joint Prior
MODEL
Joint Posterior
Posterior predictive check
18/12/2020
[Study Group] Bayesian Statistics with the Rethinking Material 12
18/12/2020
[Study Group] Bayesian Statistics with the Rethinking Material 13
